Project Info

Objective:
Design a linear classification alfgorithm that can classify cell nuclei based on 2-color (DAPI and Ki67) fluorescence microscopy images

Team Members:
1. George Agapiou (agapiou76@gmail.com)

Team Contact:
George Agapiou (agapiou76@gmail.com)

Mentor:
Tzeranis Dimitrios (tzeranis@gmail.com)

Consultants:
-

Instructions for members:

Name all files you attach with a string that starts with "Project_20152016_Ki67Classifier_".
- e.g. upload a pic of a heater as Project_20152016_ShakingIncubator_heater.png"
Write ALL your text in ENGLISH
Use as much text as necessary.. you will be graded based on quality and clarity, not quantity
Exploit the table function of wikispaces in order to organize your text and images.

Milestone 1: Single-Cell Calculations

Selection of cells in the different cell cycle phases.

Report in the biology of the problem

Using a microscope, it takes images of the population of cells, which are located in a different phase. The word “state” means a specific timeline in the cell’s life. It’s known that a cell begins its life and after a sufficient amount of time it multiplies, behaving naturally to life. This multiplication is done by geometric progression, due to the fact that when the cell multiplies it actually splits in two, it bisects. The chart below shows the life line of the cell according to the different state which is depicted.

STATE	DESCRIPTION	ABBREVIATION
Senescent	Gap 0	G0	A resting phase where the cell has left the cycle and has stopped diving
Interphase	Gap1	G1	Cells increase in size in Gap 1. The G1 checkpoint control mechanism ensures that everything is ready for DNA synthesis.
Interphase	Synthesis	S	DNA replication occurs during this phase.
Interphase	Gap2	G2	During the gap between DNA synthesis and mitosis, the cell will continue to grow. The G2 checkpoint control mechanism ensures that everything is ready to enter the M (mitosis) phase and divide.
Cell Division	Mitosis	M	Cell growth stops at this stage and cellular energy is focused on the orderly division into two daughter cells. A checkpoint in the middle of mitosis (metaphase checkpoint) ensures that the cell is ready to complete cell division.

Assuming an image from the microscope, there isn't a distinguishable way to know how many details there are , because the core by itself doesn’t have any pigment. Therefore, the core is colored with different pigments. This is accomplished by various tools which are categorized in detail below:

Antigen ΚΙ67, is a nuclear protein which is formed and is crucial with the cell multiplication. Also it’s connected to the ribosomal ΡΝΑ. The antigen’s neutralization leads to the PNA composition’s suspension. The protein Ki-67 (also known as MKI67) is a cell indicator closely connected with multiplication. While the duration of the interphase, antigen Ki-67 can be detected only on the inside of a cell’s core, whilst in the mitosis phase a bigger part of the protein is transferred on the surface of the chromosomes. The protein Ki-67 is present in the duration of all the phases of the active cell cycle (G1, S, G2, and mitosis), but is absent from resting cells (G0).
DAPI is a fluorescent coloring which is connected intensely with rich areas by adenines thymine on the DNA. It’s extensively used in microscopic fluorescence. DAPI can move intact through the cell membrane , therefore can be used on live and dead cells. Even though they move through the membrane in live cells, less efficiently.

According to what’s been stated above, the cores can be visible to microscopes and there can finally be a conclusion on the state of the cores.

Milestone 2: Linear classifier design

The issue

The issue is to calculate, by using an algorithm, the phases of a core. The data for the cores which are acquired are: the number, their location on an image and the coloring they have received. The image below shows the number of the cores, numbered about our facility.

Corresponding to the images obtained from the microscope there is a plethora of different criteria to be created in contrast to the cores, in relation to their state. These criteria can be named “measurements” of the cores. There is a considerable amount of types of measurements, where only a fracture will be linearly independent, which means that they won’t co-depend. Some thoughts for the creation of the measurements, according to the pictures received are stated below:

METRICS OF THE SYSTEM	DESCRIPTION
1. SIZE FOR EACH NUCLEUS	THE NUMBER OF PIXELS DEFINE THE AREA IN EACH NUCLEUS
2. CONTRAST ANALYSIS OF BLUE AND RED SIGNAL	WE MAKE AN OPTIONAL CONTRAST THAT DISTINGUISH EACH NUCLEUS
3. NUMBER OF HOLES	THE NUMBER OF HOLES IN RED AND BLUE SIGNAL
4. PERIMETER FOR EACH NUCLEUS	THE PERIMETER OF NUCLEUS
5. MEAN DAPI SIGNAL	MEASURE THE AVERAGE DAPI SIGNAL FOR EACH NUCLEUS
6. MEAN Ki67 SIGNAL	MEASURE THE AVERAGE Ki67 SIGNAL FOR EACH NUCLEUS

Then they appear some histograms of two few. Ki67, Size off cells

Afterwards, a multitude of cores is taken and have its category (state) set. From what has been stated above, diagrams are used for the linear independent, by utilizing the measurement 1 on the horizontal axis and the measurement 2 on the vertical axis. Using these charts, if there is a way to navigate to the known state cells, there are created areas of cell phases. Moreover, areas created, which if they had the measurement of a core and categorizes itself in that area, would mean that that core belongs in that specific phase.

Above, the known cores are created in two measurements, areas of states. Then, by using the method of quadratic discriminant analysis, result into the graph below.

According to that method, every Y class produces X data by using a multivariate normal allocation. The model assumes X data from a GAUSS allocation. For the quadratic discriminant analysis , both values , means and covariance of every category changes. This algorithm has as criteria the prediction-classification so the expected cost of ranking would be minimized.

Using the above algorithm and utilizing the linearly independed measurements 4 criteria are created and then matlab executes for all the multitude of cores and consider each core’s phase.

Milestone 3: Algorithm evaluation

The executable algorithm takes in concideration the above measurements and classifies the cores which results by the image.
For the correct utilization of the above algorithm it would be wise to report the error of its outcome. According to what has been stated , a new algorithm is created which can produce the said algorithm's error.

A method for exporting the error is :

1. By applying a population of cores which is known at which state they are.

2. By running the algorithm of its classification on the population.

3. In conclusion we compare and contrast the state of every core (G0,G1-S,G2,M) of the said population , with the state which resulted from using this algorithm.

The advantage of using this method (error of classification) is a valid estimation of the algorithm's error.